Mathematical modelling of avascular tumour growth based on diffusion of nutrients and its validation
Bibliographic record
Abstract
Abstract In this paper, a mathematical model based on the diffusion of nutrients is developed by considering the physiological changes accompanying the growth of avascular tumour. Avascular tumour growth involves the formation of three different zones namely proliferation, quiescent and necrotic zones. The main processes on which avascular tumour growth depends are: (i) diffusion of nutrients through the tumour from the contiguous tissues, (ii) consumption rate of the nutrients by the cells in the tumour, and (iii) cell death by apoptosis and necrosis. In the model, we consider the tumour to be spherical and the principal nutrients responsible for its growth are oxygen and glucose. By solving for the concentration profiles using the model developed, we are able to compute the radii of the quiescent and necrotic zones as well as that of the tumour. The proposed model is also validated using in vitro tumour growth data and Gompertzian empirical relationship parameters available in the literature. Our model is also successful in capturing the saturated volume of the avascular tumour for different nutrient concentrations at the tumour surface.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.002 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.002 | 0.001 |
| Insufficient payload (model declined to judge) | 0.001 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".